Algebra 2
Name ________________________________
STUDY GUIDE Test Chapter 12
Directions: Show all work (BE TRUE TO THE FORMULAS!) and reasoning to receive full credit.
Suppose you select a number at random from the sample space {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}. Find each probability.
1. P(less than 7)
2. P(multiple of 3 and multiple of 5)
3. P(odd or prime)
Evaluate each expression (write out the formula and/or multiplication!!!).
4. 3(4!)
Write it out:
5.
4
P3
6.
5
P2  5 C3
Formula/Work:
Answer:
Answer:
Formula/Work:
Answer:
Indicate whether each situation involves a combination or a permutation. Then solve.
7. How many ways are there to select five actors from a troupe of nine to improvise a scene?
P or C ?
Work/answer:
8.
You are looking for a new apartment. There are five apartments available. In how many ways can you schedule to inspect
three or four of the apartments?
P or C ?
Work/answer:
Use the Binomial Theorem to expand each binomial.
9.
( x  2 z)5
10.
( x  2) 3
11. A weighted coin has P(heads) = 0.4. The coin is tossed seven times. Find the probability of getting exactly 6 or exactly 7
heads.
Use the frequency table below for Exercises 15 and 16.
Birthday Months of Respondents to a Survey
Month J F M A M J J A S O N
Male
0 1 2
1 1
3 2 0 1 1 0
Female 0 1 0
1 0
2 1 3 1 0 4
12.
Find P(birthday in August | female respondent).
D
2
1
13.
Find P(male respondent | birthday in June).
Use these survey results for Exercises 14 and 15.
 Of all respondents, 20% have 0 siblings, 60% have 1 sibling and 20% have 2 or more siblings.
 Of the respondents with 0 siblings, 90% have their own room.
 Of the respondents with 1 sibling, 20% do not have their own room.
 Of the respondents with 2 or more siblings, 50% have their own room.
14. Make a tree diagram that reflects the results of the survey.
15.
Find P(share room and 1 sibling).
16. Find the standard deviation of the data by hand: 100, 98, 101, 97, 102.
17.
Of 50 people who rented clubs at a golf course, 38 were right-handed.
a.
Find the sample proportion as a percent.
b.
Find the margin of error.
c.
Find an interval likely to contain the true population proportion.
18. At a high school, 30% of the students buy class rings. You select five students at random.
a. Find P(exactly two buy rings)
b. Find P(exactly four buy rings).
19. A set of 1000 data values has a normal distribution with a mean of 29 and a standard deviation of 4. Find the following:
a. Percent of the data from 25 to 33
b. Number of data values from 21 to 25
c. Percent of data less than 37
A die is rolled. For problems 20 and 21, state whether the events are mutually exclusive. Then find P(A or B).
20. A = roll a prime number
B = roll an even number
Mutually exclusive?
Probability:
21. A = roll a multiple of 3
B = roll a number ≤ 2
Mutually exclusive?
Probability: